Lecture on
Short Stories from Quantum Information Theory

Prof. Michael M. Wolf (TUM)

The talk aims at providing a taste of Quantum Information Theory exemplified
through two problems from different branches of the field.


In the first part we will encounter quantum correlations that are arbitrarily
stronger than their classical counterparts. In physics this is related to the
foundations of quantum theory, in mathematics to Grothendieck type
inequalities within operator space theory, and in theoretical computer
science to the reduction of communication complexity. The latter perspective
suggests how - in the distant future - the scheduling of the colloquium might
be made more efficient.
The second part will shed new light on the energy gap problem from condensed
matter theory. Despite considerable effort and interest, there is basically neither
a proof technique nor a numerical method known for solving this type of problem.
We will argue that the roots of this difficulty may be deeper than expected by
showing that there are cases for which there cannot be a proof (in the sense of Gödel)
or an algorithm (in the sense of Turing).